The Romanian 2009 presidential election featured one or more high Condorcet cycles

Abstract.
With confidence≈99.7%,
the Romanian 2009 presidential election included the "Condorcet cycle"
Geoana⊃Oprescu⊃Basescu⊃Geoana where "⊃" means "majority-preferred."
B (followed by G) was the official winner. Other cycles also may have occurred;
in all there is 99.9% confidence at least one existed that contained both B & G.
With "approval voting"
(and probably also "range voting") Oprescu would have
been the most likely winner, even though he officially finished 6th.
This marks the first time a Condorcet Cycle has been detected high in
a large national election.

1. Introduction

It has been well known since the days of the
Marquis de Condorcet (1743-1794)
–
and previously clearly had been
understood by Ramon Llull (1232-1315)
–
that Condorcet cycles can exist in elections.
That is, the preferences of the voters can be such that
every candidate has at least one rival preferred over him by a voter majority.
For example, consider this 19-voter election:

Should candidate B win? One could argue "No, since
A is preferred over B by 11 out of 19 voters."
So should A win?
"No, since
C is preferred over A by 14 out of 19 voters."
So C must be the right winner?
"Still no, since
B is preferred over C by 13 out of 19 voters."

Condorcet cycles are tremendously important morally and philosophically since
they show that "naive majoritarianism" is logically untenable, since
self-contradictory. That is, it is untenable to claim
"if there are a finite number of choices and choice A is preferred by a voter majority
over choice B, then A is 'better' than B." The whole idea of "majority rule" therefore
seems to need to be discarded as a basis for "democracy."
Condorcet cycles also underlie, e.g.
Arrow's impossibility theorem
for rank-order-ballot voting systems.

This can be considered a good reason to prefer non-rank-order-ballot voting systems
not afflicted by this kind of logical paradox, unaffected by Arrow's theorem, and
obeying a different (and now logically consistent) notion of "majority rule,"
e.g. range voting.

All that was fine as a matter of abstract philosophy
– but in "real world" elections
Condorcet cycles seem to be quite rare.

Although they seem to arise considerably more
frequently in legislative votes than in single-winner public elections,
because legislators often strive to create them intentionally, e.g. they form the basis
for the "poison pill" legislative tactic.
Many examples have been documented in the writings of William H. Riker,
and see also endnote 3
of Kurrild-Klitsgaard 2001.

Indeed, in the 750 years since Llull, apparently not a single Condorcet top-cycle
has ever been clearly documented in any large governmental election!
Which leads to the question: how frequent are Condorcet cycles?
Some attempted answers are in table 2.

Table 2.
The
probability of a Condorcet top cycle (i.e the probability that no "Condorcet Winner"
exists) in various probabilistic models of elections.

Candidates are distinct points on a real line and each voter's utility function for the
candidates is an increasing-then-decreasing function of position on that line;
voting honest & odd number of voters

This absence,
however, does not necessarily prove
cycles rare. They might have been quite common but merely escaped notice!
[Actually, all it proves is that Condorcet cycles easily provable from the
usually-small subset of the full preference dataset that manages to become
publicly available,
are rare.]
Why?
Because in order to prove a Condorcet cycle exists in some election, you need to have either

rank-order-ballots,

or extensive "A versus B" pairwise-preference polling.

In fact, in the last 750 years, it is doubtful that
there have even been 100 major government
elections where
it even was possible to hope to detect a Condorcet cycle. In all the
other major government elections, the necessary
data simply was never collected, or never made public. To explain that:

1.
Elections with rank-order ballots are rare since almost all countries employ
"name one candidate" (plurality-voting-style) ballots.
But in Ireland and Australia, the top two countries using
"single transferable vote" rank-order-ballot schemes)
their governments have
refused to publish the ballot data and indeed refused even to publish
the table of pairwise-preference counts. Instead, they merely publish
certain incomplete summaries of the ballots inadequate to reconstruct these things.
These countries also will not give this data to researchers who request it.
There have been about 3 experiments
in which Ireland or Australia did publish a
full set of ballots, but in those few cases no Condorcet top-cycle arose.

2.
In countries (and there are many)
which conduct two-round "plurality+top-two-runoff" presidential
elections, it has become common
for pre-election and/or exit-polling agencies to ask pairwise questions of the form
"if it comes down to a top-2-runoff between A and B, who would you vote for?"
But it only becomes possible to
see a Condorcet cycle if
these questions are asked for enough candidate-pairs (A,B).
And usually they are not.

Our purpose here is to report the first ever observation (via the second method) of
a Condorcet cycle high in an important government election:
namely in the 2009 Romanian presidential election.

I detected this cycle
about 30 seconds after the official results were announced early in the morning of
Monday 7 Dec 2009 Romanian time,
and had been eagerly awaiting and expecting its appearance for about 5 hours.

Comments:
The "totals"
given by the Biroul
are not exactly equal to the column sums.
Also 50.33+49.66=99.99≠100, which is another error made by the Biroul.
Geoana contested his loss in constitutional court,
accusing Basescu of electoral fraud.
On 11 December the court decided to recount all 138476 invalid votes.
This recount actually slightly increased Basescu's lead
(it found 2247 ballots actually were valid,
1260 for Basescu and 987 for Geoana).
On December 14 the court
declared Basescu the victor, and Geoana conceded
defeat.

There is evidence
that some fraud occurred, although it does not amount to a large quantity; Geoana
suggests those with more evidence send it to fraudarealegeri2009@gmail.com.
I personally am convinced based on exit polls that
the fraud, if any, was small in percentage terms
– but unfortunately, only a small fraud was needed.

'Instant' runoff (IRV)
would immediately have eliminated everybody except Basescu, Geoana, and Antonescu
(since the sum of all their top-preference votes failed to exceed Antonescu's 20.02%).
However, it is not obvious whom IRV would have eliminated next.
Asset voting would presumably have elected Geoana since –
somewhat unexpectedly –
Antonescu, Marko, and Becali all endorsed Geoana in the G vs B runoff.
(Antonescu called Geoana the "lesser evil" and denounced Basescu as a
"demagogue and a populist." Oprescu also argued Geoana was the lesser evil, but
refused to fall into the trap of [therefore] endorsing him, since in Oprescu's view both G and B
were "false Romanians.")
Evidently, though, Romania's voters were mostly unmoved by those endorsements.

3. Pairwise Polls

The principal pollsters and their pairwise-style pre-election polls are reported
in the following tables.

Unfortunately, the media simply invented some fake "results" for "polls"
which never actually happened. E.g. CURS and CCSB both
posted warnings on their web pages about that.
Multiple media coverage of the same "poll" does not necessarily prove that poll existed since
different media outlets copy each other.
It is preferable to check primary sources
(i.e. the polling firms) in all cases and distrust media accounts –
or at least, only
rely on the media which actually sponsored that poll!
Unfortunately, I have not always been able to do that, but I have done it
for all the polls in the most important and critical tables 7, 9, and 11, the online
polls, and the Gallup polls in §5.

Table 4.
Important polling firms in Romania, and media or political
entities that sponsored their efforts in 2009.

Comments:
Sometimes pollsters conduct and publicize polls without being paid for it by anybody,
for public relations, self-calibration, and/or advertising purposes.

Some Romanian conspiracy-theorist bloggers and media have insinuated that
INSOMAR is supported by
Sorin Ovidiu Vantu (the "media mogul" who owns Realitatea TV and who was linked
with Geoana) while CCSB is 67% owned by
Camelia Voiculescu, the daughter of another media "mogul" whom Basescu also accused
(during a G-vs-B debate)
of associations with Geoana and a founder of the PC
– and therefore, their polls should not be
trusted. (And indeed, the CCSB and INSOMAR polls comparing Geoana versus Basescu were
the ones with the most outrageous pro-Geoana errors, while Gallup, CURS, and
CSOP basically got correct answers.)
Fortunately, the reader may verify that even if all CCSB and INSOMAR polls are discarded
from our dataset, the main conclusions of this paper will not be greatly affected.

The problem in a nutshell is this:
there are two different voter-populations (a) the voters in the official B-vs-G runoff
and (b) the pollsters' attempts to get representative samples (with different pollsters
using different techniques).
Our statistical analyses will all be predicated on the assumption that (a) and (b)
are the same. But at least in the case of the largest INSOMAR polls, table 5
indicates differences existed.

The usual patter about why such conspiracy theories are dubious
is that pollsters are very motivated by market forces
– especially in the case of publicly-released "showcase"
polls like these – against delivering wrong/inaccurate answers; and
further, there is little motivation to fake poll results anyhow
(since, e.g, there is no logical reason why a poll wrongly predicting a Geoana victory,
would motivate anybody to vote Geoana in a G-vs-B election).
Indeed, I would expect that CCSB and INSOMAR will now be punished by
having fewer market research
customers.

The fact that, in some cases, different polls disagreed, means
that anybody aware of only a subset of those polls, risks being deluded.

Comments:
The polls in table 5 are unnecessary for the purposes of this paper,
since they all are trumped by the official runoff election count, which is allegedly exact.
We give this table purely as a check on the non-fraudulence of the official count or on the
abilities of the pollsters.
The CURS, CSOP, and Gallup polls got the right answer.
The two large INSOMAR polls at the end both were far outside their expected margins of
error, suggesting either (a) election fraud by Basescu, or (b) some kind
of sampling bias by the pollsters relative to the true voter distribution, or (c)
the pollsters lied.
Probably the reason is mostly (b) because 4 exit polls
of the runoff (which presumably has greatly reduced biased-sampling problems)
found: INSOMAR 48.8%, CSOP 50.4%, CURS 49.3%, CCSB 49% respectively for Basescu.
These exit polls overall still wrongly predicted a Geoana victory, but much less
dramatically than the pre-election polls, indeed their errors seem within
the margin of error; and Basescu claims his victory was due to the 146876 valid votes from
Romanian voters residing in foreign
countries (who voted in B's favor about 78.9% and presumably were never polled).
Note that Basescu's official winning margin over Geoana from table 3 was 70048 votes
(0.66%);
and without the foreign voters, B actually would have lost to Geoana
by 14738 votes (0.14%).

Comments:If the samples were independent and from the correct voter distribution,
and if we were allowed to ignore the annoying rounding of the pollsters' figures,
then, based on the polls after mid-october,
the confidence Antonescu was genuinely majority-preferred over Basescu would be
over 5.5σ, that is
over 99.999998% confidence.
By the use of "optimally weighted stratified sampling" techniques
(see CRV Puzzle #101; at least some pollsters,
e.g. Gallup, have claimed they employ these techniques)
pollsters should achieve error bars actually below the Bernoulli variance
formula we are employing,
therefore our conclusions ought to be valid.

According to Bernoulli,
given N pollees a fraction p of whom answer "yes" and q=1-p of whom answer "no,"
the estimated mean-yes fraction in the larger universe is p and the estimated variance
in that estimate is σ²=pq/N.
Concerning the value of N, note that in 14 poll-questions
mentioned in this paper whose response rates were provided by the pollster,
the mean response rate was 64%. Therefore I employ N=0.64T
where T is the total number of pollees, as my estimate of N for polls where the pollster
did not inform us of the response rate.

However, the poor performance of some of the pollsters
in table 5 at predicting the official runoff result
contradicts that and casts some doubt on their expertise and on all our conclusions.

Indeed, the B-vs-G polls tabulated after mid-October would
have yielded about 10σ "confidence" of a majority-preference for G over B.
The official count actually found
a slight G>B majority among the non-foreign (i.e the polled)
Romanian voters – Basescu won due to foreign voters – but
the polls found about 9.6σ "confidence" it should have been larger than it was.

Comments:If the samples were independent and from the correct voter distribution,
and if we were allowed to ignore the annoying rounding of the pollsters' figures,
then, based on the above 3 polls,
we get about 0.5σ confidence that Antonescu was
majority-preferred over Geoana,
which is
only 70% confidence.
On the other hand if we only
employ the November polls (which both were available rounded to
±0.05% accuracy, unlike the CURS poll) then it is Geoana who wins, albeit
with only 56% confidence. We shall do the latter.
The habit of pollsters of rounding to the nearest integer
percent may be naively appealing (if, say, their error bar is ±2.6%)
but is a very bad practice since it severely handicaps efforts to compute
confidence values or to combine data from different polls. CURS did not
respond to requests for more accurate data.

Comments:If the samples were independent and from the correct voter distribution,
and if we were allowed to ignore the annoying rounding of the pollsters' figures,
then, based on the above after-mid-october polls,
the confidence Oprescu was genuinely majority-preferred over Basescu would be
3.15σ,
that is
99.92% confidence.
Press coverage of the
CURS poll commented that "paradoxically, Geoana has the best chances to
get in the runoff but [once there] would have smaller chances than either Antonescu or
Oprescu to defeat
Basescu." This paradox is highly related to the Condorcet cycles.

Table 9.
Head-to-head polls (listed in chronological order): Geoana vs Oprescu.
All polls agree Geoana wins this matchup.
There also was a press report of a "subjective estimate" by Gallup Romania that
Geoana and Oprescu would each get 50% in a head-to-head runoff, but
I could not find any actual Gallup poll backing that estimate with genuine data.

Pollster

Date 2009

Sample

Geo

Opr

CURS

15-22 Oct

1110 face-to-face interviews in their homes, but only 66% responded

53%

47%

INSOMAR

1 Nov

1207 over age 18, but only 653 answered

54.8%

45.2%

Comments:If the samples were independent and from the correct voter distribution,
and if we were allowed to ignore the annoying rounding of the pollsters' figures,
then, based on the above 2 polls,
the confidence Geoana was genuinely majority-preferred over Oprescu would be
about 2.86σ,
that is
99.79% confidence.

Finally, there appears to have been no reputable
polling organization that did a head-to-head comparison between
Oprescu and Antonescu.
But there were two online internet polls (anybody on the
internet could participate)
addressing this question.

These polls obviously cannot be taken seriously because they both were from extremely
unrepresentative, pro-Antonescu biased, samples which would have
Antonescu defeating all rivals (except perhaps Cernea!)
by huge margins, e.g. in the first poll defeating Basescu pairwise by 88.6% to 11.4%.
However, it is perhaps of interest that Antonescu would according to
the first poll defeat Oprescu by smaller margins than those by which either O or A
defeated Basescu.
In the second poll, Antonescu defeats Oprescu by a smaller margin than he defeats
Geoana (albeit by a slightly larger margin than his defeat of Basescu).
These facts suggest that in an unbiased sample, Oprescu might defeat
Antonescu. This same speculation also is supported by Gallup's approval-voting-style
poll discussed in our §5.
Therefore we shall estimate (because this is the estimate arising from the Gallup approval poll)
that Oprescu would win a matchup against
Antonescu with probability 89%. Observe that in that poll (restricting attention to
the 72-73% pollees who provided a response) at least 1.55% approved Oprescu but not
Antonescu, and at least 1.55% disapproved A but not O. Hence
in a pairwise A-vs-O contest, we suspect that
O would win by at least (as our mean estimate of a lower bound)
51.55-to-48.44%.

4. The Condorcet Cycles and Pairwise Table

Table 10a.
Pairwise-margins table (best estimates) for Antonescu, Basescu, Geoana, and Oprescu.
Figures represent the estimated vote percentage for the
candidate in that row, in a head-to-head matchup with the one in that column.
They are based on polls after mid-october only, and in the Geo-vs-Ant and Geo-vs-Opr cases
only on polls whose genuineness has been confirmed;
the Bas-vs-Geo result is the exact
official runoff result.
Apparently there was no Ant-vs-Opr poll but indirect
evidence suggests Opr would have had better chances (estimate 89%)
in that matchup and won it by at least 51.55%.
Error bars are 1 standard deviation.

Ant

Bas

Geo

Opr

Ant

***

52.07±0.37

49.78±1.36

≤48.44

Bas

47.93±0.37

***

50.33±0

48.24±0.56

Geo

50.22±1.36

49.66±0

***

53.85±1.34

Opr

≥51.55

51.76±0.56

46.15±1.34

***

Table 10b.
Pairwise-defeat-confidence table for Antonescu, Basescu, Geoana, and Oprescu.
Figures PRC represent the confidence the
candidate R in that row would win a vote-majority versus the
candidate C in that column, in a head-to-head matchup.
From now onward (for better or worse) we shall regard these probabilities PRC
as independent of each other.

Ant

Bas

Geo

Opr

Ant

***

99.999998%

44%

11%

Bas

0.000002%

***

100%

0.08%

Geo

56%

0%

***

99.79%

Opr

89%

99.92%

0.21%

***

What about the foreign voters?
Foreign voters boosted Basescu's margin over Geoana by 0.80%
(from -0.14% to +0.66%).
According to
Alina Mungiu-Pippidi
(Democracy Studies Chair at
Hertie School of Governance in Berlin, and a Romanian)
expatriate Romanians automatically vote heavily
against parties linked to the old communist regime,
which in this case means they automatically vote against Geoana.
However, this presumably would not have motivated voting against either Antonescu or Oprescu.
A different theory about the expatriates is that many live in Moldova, and since
Basescu has loudly championed the right of Moldovan Romanians to get Romanian citizenship,
they support Basescu.
Presumably that motivation to vote for Basescu would still apply.
If one guesses (which we shall not) that the same
boost would have occurred for Basescu versus either Antonescu or Oprescu, then
that would have diminished the Ant⊃Bas vote from 52.07% to 51.67%
and decreased the confidence of the "⊃" to 4.5σ (99.9997%);
and it would have diminished the
Opr⊃Bas margin from 51.76% to 51.36%
and diminished the confidence to 2.43σ (99.25%).
This is not enough diminishment to hurt the main conclusion
of this paper, i.e. that a B&G-containing cycle existed with confidence≈99.9%.

From this we conclude with confidence 99.87% that at least one of these two cycles
genuinely exists, i.e. with confidence 99.87% the official winner Basescu,
and the official runner-up Geoana, both were
members of at least one of these two cycles.
Also there are additional possible cycles (such as B⊃G⊃O⊃A⊃B,
which has estimated 89% chance of being genuine, almost independently
of P1), which pushes
the probability of at least one G&B-containing cycle really existing up
over 99.9%.

To be precise about this, the exact formula (got by writing it
as a sum of 64
monomial terms, each a product of 6 probabilities and
expressing the probability of a directed-graph configuration
among the 4 vertices {A,B,G,O}, where all configurations not including a cycle are
multiplied by zero; then simplifying using PBG=1)
for
the probability that at least one of the three cycles
O⊃B⊃G⊃O
or
A⊃B⊃G⊃A
or
A⊃B⊃G⊃O⊃A
is present is

With the PXY in table 10b this yields Prob(BGcycle)=99.904%;
and even if we instead use the decreased values
PAB=99.9997% and POB=99.25%
due to a postulated foreign pro-Basescu vote, we still get
Prob(BGcycle)=99.871%.
It's important to realize that despite the unclarity about the pairs A-vs-O and
A-vs-G, we still get high confidence of cycles, mainly
because the leading cycle candidate
O⊃B⊃G⊃O
does not involve either unclear pair.

The confidence that no Condorcet winner existed is at least 56%.
Almost all of the remaining 44% probability would represent the chance that Antonescu was
really the Condorcet winner. However, that estimate of "44%" is ignoring the possibility that
Antonescu would lose in a head-to-head comparison with Oprescu.
Although I am unaware of any
reputable polling directly
addressing that question,
from the online polls corrected to remove pro-Antonescu bias, and also from the
Gallup approval-style poll,
it appears that Oprescu would have 89%
chances in an A-vs-O matchup. (There also is a small chance
Antonescu might also lose pairwise versus any
of the other candidates such as Tudor, Kelemen, etc.)
In view of this, we reduce this 44% chance to
5%≈PAOPAGPAB.
(More precisely, we find a 5.02% chance that a Condorcet winner exists, in which case there is
96% chance it is Antonescu, 4% chance it is Oprescu, and negligible chance it is anybody else.
PAOPAGPAB is the exact probability it is Antonescu,
POAPOGPOB is the exact probability it is Oprescu,
[among [A,B,G,O}],
etc. and these probabilities may be added since they represent disjoint events.)
So our final estimate of the chance
that no Condorcet winner existed is 95%.

What sort of Condorcet cycles were these? "Laatu types":
Juho Laatu (after reading an earlier draft of this paper)
proposed classifying Condorcet cycles in large elections into three types:

I.
"Weak" cycle (aka random cycle or noise-generated cycle):

the looped candidates are almost tied

can be a result of some almost random variation in the votes

one could say that this kind of a loop is one special version of a tie

any of the looped candidates could be the winner (with no big violation
of any of the majority opinions)
against any

there is some specific, in principle describable,
reason that has led to the formation of this
loop (not random variation in the votes)

the cycle / opinions are strong enough to that they are unaffected by
daily/weekly random opinion fluctuations

III.
"Strategic" cycle:

artificially generated by strategies employed by some voters to
"game the election"

not based on sincere opinions

Which kind of cycle do we have here in Romania 2009?
I do not believe the O⊃B⊃G⊃O cycle is "weak" and "noise-generated"
because, if the votes were just the results of 107
voters tossing independent identical coins we would expect margins
(and "noise levels") of order ±3162 votes, i.e. ±0.03%.
The vote-margins in this cycle instead were about
3.5%, 0.66%, and 7.7% respectively – far larger.
I believe this cycle was stable from day to day and there were some
underlying rational reasons behind it.
Indeed, any cycle detected via polls rather than exact vote counts
will necessarily (if its detection is statistically significant) not be "weak"
in Laatu's sense.

It also seems not "strategic" since its pairwise claims are based
on 2-choice polls and elections, in which it is difficult or
impossible to see any strategic reason for the pollees/voters to be
dishonest.

On the other hand, obviously the huge distortions in the official
round-1 plurality-counts away from the underlying truth, were mostly caused by
strategic decisions by voters arising because of the well-known flaws in
plurality as a voting method. With the plurality+top2
method employed, voting for anybody not perceived to be in the "leading three"
in terms of election chances, was a "wasted vote." When the decision was made (almost
certainly as part of a deal between the major political parties and media moguls)
that only Antonescu, Basescu, and Geoana
would be allowed to participate in a widely publicized and televised debate, they
immediately became the leading three, regardless of whether
anybody else was felt by Romania to be a superior candidate, and Oprescu's doom
was sealed. Then:
Because Basescu had a large lead in plurality-style polls going into round 1
(but clearly not large enough to get a majority and thus avoid the runoff)
while (pairwise poll data showed)
Antonescu was more likely than Geoana to defeat him in the runoff,
it became strategically the smart move for many Basescu supporters to vote for
Geoana in the first round, even if they honestly felt Geoana was the worst candidate.
Meanwhile, anti-Basescu voters would have been motivated to vote Antonescu, even
if they honestly preferred Geoana.

Therefore, the cycle was "strong" (Laatu type II).
Nevertheless, it was not very "strong," since
0.66%, 3.5%, and 7.7% represent small to moderate margins.

All of Laatu's three types do occur:
Bochsler 2008 found a preference cycle

{P or A}⊃S by 109812 to 102796 (51.6% majority)
S⊃P by 106832 to 104144 (50.6% majority)
P⊃A by 106863 to 101586 (51.1% majority)

in a 3-choice referendum about changing a law about state employees
held on 28 November 2004 in the Swiss Canton of Bern.
(This election was held using unusual "decision tree" style ballots, which
was the reason the cycle was detectable.)
Bochsler in his paper explained the reasons he believed
this cycle was Laatu type III, i.e. was mostly caused by "strategic voters"
trying to "game" the decision-tree election.

Kurrild-Klitsgaard 2001 found a cycle

E⊃J by 50.6% majority among the 77% respondents among the 1169 pollees
J⊃R by 51.1% majority among the 92% respondents among the 1169 pollees
R⊃E by 52.8% majority among the 89% respondents among the 1169 pollees

among the three candidates {Hans Engell, Uffe Ellemann-Jensen,
and Poul Nyrup Rasmussen} for Danish Prime Minister in mid-May 1994.
Note that (a) the Danish PM is not elected by the people, hence this poll had nothing to do
with any real election, (b) the ±1σ margin of error for this poll was
±(15-16) votes,
i.e. ±(1.52% to 1.67%),
so that the statistical confidences that these "majority" preferences
genuinely existed, were respectively 64%, 76%, and 96%.
This is of course laughable for the purpose of drawing any conclusion about the
"reality" of this cycle in the Danish electorate. But it is legitimate to remark
that among these 1169 pollees alone there was a cycle. But if so, there is
no evidence it was not merely "noise-generated," i.e. of Laatu type I. Similarly, in
the June 2008 election by the
Wikimedia Foundation to fill a vacant seat on its Board of
Trustees (Schulze's beatpath
Condorcet method with rank-order ballots was employed),
there were 15 candidates, about 26000 eligible
voters, and 3019 valid ballots.
Ting Chen was the clear Condorcet
winner hence won the seat, but there was a cyclic tie for sixth
to ninth position between J.Heiskanen, R.Postlethwaite, S.Smith, and
R.Saintonge: JH⊃RP⊃SS⊃RS⊃JH.
However
reversing only 5
pair-preferences
on ballots would have eliminated the cycle.
Thus, again, there was no evidence this cycle was not
"noise generated," i.e. Laatu type I.

What were the underlying rational reasons behind our
cycles?
That is very difficult to ascertain
(or even merely to verify), especially for a foreigner like me unfamiliar with the
Romanian language.
But it is not hard to invent a plausible-sounding story "explaining" a cycle.
There is a comparative sketch of
the candidates here:
http://RangeVoting.org/Romania2009MainCanddts.txt.
Consider these three issue-sets (call them
T1, T2, T3):

Foreign relations & diplomacy. Pensions and unemployment benefits.

Accusations of corruption and cozy relations with media moguls &
wealthy businessmen; worries about trampling constitutional limits on power;
best for hospitals & schools; feeling that
Romania's current leaders doing poor job so need a change.

Desires to cut government size and budget;
racist preferences for Christianity over Islam;
Moldovans who want an easy path to Romanian citizenship;
expatriate Romanians who automatically vote against parties linked to the old communist regime.

Voters caring mostly about
T1 would have preference order G>B>O.
Voters caring mostly about
T2 would have preference order O>G>B.
Finally, voters caring mostly about
T3 might have preference order B>O>G
and apparently B was felt to have won his final debate with G.

If these three kinds of voters were roughly equinumerous, that would produce
an O⊃B⊃G⊃O cycle. I do not claim this is the right, true,
or only explanation; I merely say it is one possible hypothesis.

5. Approval- and range-voting style polls

Gallup Romania during 5-8 November
conducted both an Approval-voting-style poll
and a Plurality-voting-style poll (1253
adults [age≥18] representative of the Romanian voter population; "stratified sampling"
techniques used; face-to-face interviews at their homes),
and the two graphics (provided by Gallup) give the results.

Comments:
Oprescu and Antonescu are clearly ahead of everybody else in the approval-style
poll. Oprescu had
more approvals than any rival despite having the fewest (only 72%) pollees
giving an opinion about him; and Oprescu also had the fewest disapprovals even
after rescaling to discard all no-opinion votes.
Antonescu is second, and Geoana third; all others are statistically-significantly behind,
i.e. they would all lose with confidence exceeding 99.9%.
To assess this more precisely,
I did a Monte Carlo calculation. It indicated that the Gallup data predicts
that, with confidence≈89.5%,
Oprescu would defeat Antonescu in an approval-voting election;
and with confidence≈99.4%
Oprescu would defeat Geoana.

But with plurality voting the poll predicts Basescu wins
(also with confidence>99.9%), which, of course, indeed happened in round 1.
Observe that switching from approval to plurality voting swaps the
fourth and first place finishers Oprescu and Basescu.
I.e, Oprescu comes top and Basescu bottom among {A,B,G,O}
in the approval-voting poll, exactly the opposite of the official results
using plurality + top-2-runoff voting.

I am unaware of any range-voting-style polls.
However, a
poll by IOP (1355 telephone & face to face interviews, 20-23 October)
asked a range-voting-like question "How much do you trust politician X?"
("Cata incredere aveti in X?") for many different X on an 0-100 trust scale.
The most-trusted
among the presidential candidates again was found to be Oprescu (37%).
Oprescu had also been the most-trusted (48%) in an earlier (18-25 Sept) IOP poll
asking the same question.

Other remarks:
The polls I examined revealed no sign of a "gender gap."
But there was an "age gap" with older voters favoring Geoana and younger ones Basescu.

6. Conclusions

The 2009 Romanian Presidential Election probably exhibited
two or more different
Condorcet cycles.
I find about 99.9% confidence (assuming
valid polls) that both of the
top two official finishers Geoana & Basescu were members of at
least one cycle.

There either was no Condorcet winner (95% confidence) or it was the official third-placer
Antonescu (4.8%) or 6th-placer Oprescu (0.2%).

The official plurality+top2runoff (2 round) method used, elected
Basescu who would have lost head-to-head versus either O or A by
comparatively clear margins; B did beat G pairwise but only by an
0.66% margin. So, based on the pairwise table alone, B overall was
probably the worst choice among {A,B,G,O}, but was elected; while A or O were
probably the best choices, but finished third and sixth, respectively,
in the official count.

The truth was this was a close 4-way race between {O, A, G, B}
but the
election method distorted that hugely and made it look like (and effectively be)
a 2-way race between G & B, with O & A far behind.

The only approval-voting-style
poll I have found says if it had
been approval voting
then O, A, and G all would have placed clearly ahead of B. So again, the
official winner B appears to have been the worst choice. The approval
poll, and also two range-like
"trust level" polls, all gave the top spot to O
despite the fact that Oprescu
officially finished last among these four (and 6th overall) with only
3% of the vote.
So approval and the officially-employed plurality+top2runoff method
featured reversed results for the top
and bottom candidates among these 4.

With
instant runoff voting (IRV),
one of {A,B,G} would have won, but it is unclear who.
With
asset voting, presumably Geoana would have won.
I thank Ronald Rivest for informing me that (with the central estimates of the pairwise margins
in table 10a) under both Borda Count and Schulze's "beatpath" Condorcet method,
Geoana would have won.

7. Acknowledgments

I thank
Daniel Bochsler,
Juho Laatu,
Alina Mungiu-Pippidi,
Diana Viasiu,
as well as some other Romanians who wish to remain anonymous, for useful comments.

Nicolaus Tideman: Collective Decisions and Voting: The Potential for Public Choice, Ashgate 2006.
For my recalculations of his cycle-probability estimates in chapter 9, see
http://RangeVoting.org/TidemanElModel.html.